Finite Means Research Articles

Crack fault diagnosis in rotor bearing system by transient and study state time domain analysis

Online condition monitoring methodologies for rotor dynamic systems are an emerging trend and an essential for safe system operation. During operation fatigue cracks in rotor shaft can lead to catastrophic failures if not identified at early stage. Therefore, these systems require a reliable crack fault detection methodology. The vibrations may induce in the system due to different type of faults, like shaft transverse cracks, oil whirl and whip. To make the detection methodologies robust and reliable, redundancy in crack detection methodologies is vital. The present research is a foolproof procedure to detect the travers fatigue crack in the rotor shaft. Rotor response, orbital pattern, and response FFT during transient (runup/cost down) and study state operations at 2X & 3X sub critical speeds are analyzed to identify the presence of crack in rotor bearing system. The rotor system is analyzed by numerical Finite Element Modeling (FEM) simulations and experimental means. Open Wedge Crack (OWC) and Breathing Wedge Crack (BWC) are modeled and their behavior is studied. The effectiveness of Newton Rapson method, Houbolt numerical method, and Harmonic Balance Method (HBM) in crack diagnosis are studied. Numerical FEM results are validated with experimental and published literature results. FEM simulated and experimental response FFT shows similar response behavior with presence of crack with 98 % correlation and less than 2 % error. FEM simulated and literature response orbital pattern at 2X sub critical backward speed are similar with less than 3 % error (97.76 % close) and at 2X sub critical forward speed are similar with less than 1 % error (99.33 %).

Estimation of finite population mean using double sampling under probability proportional to size sampling in the presence of extreme values

Values that are too large or small enough can be found in many data sets. Therefore, the estimator can yield ambiguous findings if several of the incredible deals are picked for the sample. When such extreme values occur, we propose improved estimators to determine the finite population means using double sampling based on probability proportional to size sampling (PPS). The properties of estimators are obtained up to the first order of approximations. When the size of the units varies widely, the PPS sampling technique may be employed. To determine the values of Pi when using PPS, we must be acquainted with the aggregate of the auxiliary variable Xi. However the designs and estimation techniques we have looked at so far are unsuccessful and are less effective when this information is difficult to locate or when other information is missing. The two-phase approach is preferable and more feasible in these kinds of circumstances. To demonstrate how effectively the recommended estimators performed, we used three actual data sets. We show mathematically and theoretically that the suggested estimators outperform alternative estimators.

Skuteczność prawa i problemy jej badania

Any action shall be efficacious when it attains in a sufficiently high degree the purposes defined by a person undertaking it. From this point of view we may also discuss the efficacy of law (of a legal rule, of a group of legal rules, of a system of law) being a result of a purposful activity of a legislator. The Au- thor presents an analysis of the efficacy of law understood as prohibitive and imperative rules, with the assumption that the purpose of the legislator was sufficiently precisely defined.As a basis for the typology of the efficacy of law a differentiation was made between: direct purposes (i.e. conduct conformable to a rule) and indirect pur- poses (consequences of the conduct conformable to a rule) as well as between subjective purposes (i.e. behaviour, feelings and attitudes) and objective purposes (other purposes).Psychological efficacy of law means the influence of the information about a given rule on feelings and attitudes of an addressee of the rule regardless of whether this leads to conduct conformable to a rule or not. Behavioural efficacy means that a direct purpose of a given rule is realized because the information about this rule motivated its addressee. Finite efficacy means that an indirect objective purpose is attained, in another words, that a definite situation being a consequence of the attainment of the direct purpose is created. Socio-educational efficacy or law means attainment of the subjective indirect purpose by evoking certain attitudes, of an addressee of legal rules or of other persons.The Autor presents an analysis of assumptions and conditions to be made while studying the above mentioned kinds of the efficacy of law. Preparing scales with the aim of measuring each of these kinds of efficacy needs meeting various complex conditions. Because of the difficulties, in practice partial indica- tors of the efficacy of law are commonly used. A typical one to cite is a quan- titative analysis of conducts contrary to the law, the constatation of which is an assumed function of the organs applying the law.

Limit theorems for negatively superadditive-dependent random variables with infinite or finite means

<abstract><p>The author studies the laws of large numbers for weighted sums of negatively superadditive-dependent random variables. The obtained results in this paper extend and improve the corresponding theorems of Yang et al. [Commun. Stat. Theor. M., 48 (2019), 3044-3054]. Moreover, the author obtains a new theorem of mean convergence for weighted sums of negatively superadditive-dependent random variables, which was not considered in Yang et al. (2019).</p></abstract>

Estimation of Finite Population Mean in Simple and Stratified Random Sampling by Utilizing the Auxiliary, Ranks, and Square of the Auxiliary Information

In this article, estimating the finite population means under simple random and stratified random sampling schemes. Our proposition is based on the notion of using auxiliary information in a more rigorous fashion. Specifically, we use ranks and squared values of the auxiliary information in addition to observed values of the auxiliary variable. The applicability of the proposed family of estimators is demonstrated by considering real data sets coming from diverse fields of applications. Moreover, the performance comparison is conducted with respect to a recently proposed family of estimators. The findings are encouraging and superior performance of the suggested family of estimators is witnessed and documented throughout the article.

Production of Sustainable Renewable Energy from Biodegradable Wastes

Renewable energy from ISWM system plays a significant role in clean energy harvesting. SW containing 50% - 60% of methane (CH4) gas, with 40% - 50% carbon dioxide (CO2). CH4 being a valuable resources for clean energy production has 18 - 22 MJm-3 of energy content. Nigeria depends on finite means of energy sources, and are generally non-renewable in nature. Hence, this poise a greater danger to environmental sustainability. Therefore, this research aimed at providing an effective and sustainable dependability from the use of non-renewable to renewable energy sources, leading a shift from oil resource based energy to biodegradable energy & W-t-E resources, all emanating from MSW. Quantitative and qualitative approaches have been adopted in-line with this research work, to effectively evaluate and to extract 100% of CH4 gas (natural gas) available as LFG from SW to be used in domestic, industrial and power electricity generation plants. Technically this is achievable through passive or active gas management system, for an extensive extraction peak productivity period of 1 - 20 yrs. of available waste stream table 3, figure 4 and 7. Similarly an increased waste generated in 2020 from that of 2015, led to the extraction peak production period of 1 – 30 yrs. of continuous energy harvesting table 4, figure 5 and 7 respectively. Hence, there is the need for various stakeholders to invest in effective ISWM to boosting raw material sources for RRR.

Effect of the Location of Broken Wires on Prestressed Concrete Cylinder Pipes under Working Pressure

The precise analysis of the overall mechanical performance of prestressed concrete cylinder pipes (PCCPs) with broken wires is a complicated problem. In this article, powerful finite element numerical means are applied to solve this problem. Firstly, the advantages and shortcomings of the current prestress simulation methods in the finite element analysis (FEA) literature are discussed, and the initial stress method based on a novel single-spring joint element method to model the pre-stress of wires is proposed. Then, different distributions of broken zones, including random broken distributions, are developed for two typical PCCP pipes with different wire-wrapped layers. The established nonlinear FEA model considers actual service processes such as manufacturing, installation and operation to investigate the mechanical behavior of two typical PCCP pipes with different breakage distribution regions and breakage ratios, and in particular, the overall mechanical behavior of a pipe with random breakage is determined first. To verify the accuracy of the proposed pre-stress simulation method and the established nonlinear finite element model, the overall mechanical response of a pipe before wires broke is compared with the results obtained via the specifications. The computed results under the corresponding breakage assumptions are consistent with the conclusions in the existing literature, providing important guidance for pipeline management and operation.

Shifting and Expanding Clause Combining Strategies in Heritage Turkish Varieties

Turkish is a language described as relying predominantly on non-finite subordination in the domain of clause combining. However, there are also strategies of finite subordination, as well as means of syndetic and asyndetic paratactic clause combining, especially in the informal settings. Clause combining is and has been one of the focal points of research on heritage Turkish (h-Turkish). One point is particularly clear: In comparison with the monolingual setting, finite means of clause combining are more frequent in h-Turkish in Germany, the U.S., and the Netherlands, while non-finite means of clause combining are less frequent. Overall, our results confirm the findings of earlier studies: heritage speakers in Germany and the U.S. prefer paratactic means of clause combining using connectors, as opposed to monolingual speakers. Our results also reveal that age (adolescents vs. adults) and register (informal vs. formal) significantly modulate the use of connectors. Moreover, we find that the shift in preferences in means of clause combining triggers an expansion in the system of connectors and leads to the development of new narrative connectors, such as o zaman and derken. The system of syndetic paratactic clause combining is expanding in heritage Turkish. This expansion calls for multifaceted modeling of change in heritage languages, which integrates language-internal factors (register), dynamics of convergence with the contact languages, and extra-linguistic factors (age and language use).

On The Efficiency of Ratio Estimators of Finite Population Mean Using Auxiliary Information

Ratio estimation is a technique that usages available auxiliary information which is certainly correlated with study variables. In this study, a class of ratio-type estimators of finite population means has been anticipated to solve delinquent of estimation of the population mean. Properties of anticipated estimators namely Bias & Mean Square Error were acquired up to the first order of approximation & the condition for their efficiency over some existing estimators was also established. The results show that anticipated estimators are enhanced & proficient (minimum mean square errors) than other estimators with the highest precision.

Integration of Nonprobability and Probability Samples via Survey Weights

Probability sample encounters the problems of increasing cost and nonresponse. The cost has rapidly been increasing in executing a large probability sample survey, and, for some surveys, response rate can be below the 10 percent level. Therefore, statisticians seek some alternative methods. One of them is to use a large nonprobability sample (S_1 ) supplemented by a small probability sample (S_2 ). Both samples are taken from the same population and they include common covariates, and a third sample (S_3 ) is created by combining these two samples; S_1  can be biased and S_2  may have large sample variance. These two problems are reduced by survey weights and combining the two samples. Although S_2  is a small sample, it provides good properties of unbiasedness in estimation and of survey weights. With these known weights, we obtain adjusted sample weights (ASW), and create a sample model from a finite population model. We fit the sample model to obtain its parameters and generate values from the population model. Similarly, we repeat these processes for other two samples, S_1  and S_3  and for different statistical methods. We show reduced biases of the finite population means and reduced variances.as the combined sample size becomes large. We analyze sample data to show the reduction of these two errors.

Deterrence against Terrorist Attacks in Sports-Mega Events: A Method to Identify the Optimal Portfolio of Defensive Countermeasures.

Sports mega-events, such as the Olympic Games or the Super Bowl, are attractive targets for terrorist organizations, due to their visibility, size, and number of people involved. Two characteristics of sports mega-events, however, make them distinctive in comparison with other well-studied target protection problems in counterterrorism analysis (such as transportation hubs or infrastructure facilities). First, defensive measures are often publicly known. Second, their finite horizon means that deterrence against any attack must be prioritized. In this article we thus propose a method that identifies the best portfolio of defensive measures the defense may adopt, given a fixed budget, to minimize the chances of suffering a terrorist attack during a sports mega-event. The method makes some relevant contributions to adversarial risk analysis: (i) it represents attackers that can choose among multiple attack scenarios and the no-attack scenario; (ii) it measures the deterrence effect caused by synergic portfolios of defensive measures; and (iii) it proposes an algorithm that identifies dominated portfolios and may, thus, overcome the scalability problems inherent to this portfolio optimization. We apply this method to a real-world defense problem, revisiting the defensive countermeasure planning for the 2016 Brazilian Olympic Games in Rio de Janeiro, Brazil. In the case study, we find a nonlinear relationship between budget expenditure and deterrence, as well as a decreasing marginal effectiveness use of resources after a given budget threshold, which would support a more efficient allocation of investments in the Gamesdefense.

LRS Bianchi type-I bouncing cosmological models in f(R,T) gravity

In this work, we have investigated the cosmological bouncing solution in LRS Bianchi-I space-time in framework of [Formula: see text] gravity. Our study in this paper is based on the modeling of matter bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. Mathematical simulations have been done in the modified general theory of relativity in the form of [Formula: see text] theory proposed by Harko et al. [f(R, T) gravity, Phys. Rev. D 84 (2011) 024020], whose functional form is as [Formula: see text] where [Formula: see text] is Ricci scalar, [Formula: see text] is trace of energy–momentum tensor and [Formula: see text] is constant. Taking the non-vanishing scale factor in LRS Bianchi-I space-time, the geometrical parameters such as Hubble parameter and deceleration parameter have been derived and their subsequent use in the expression of pressure, density and EoS parameter [Formula: see text] confirms qualitatively the initial conditions of the universe at the bounce. With the non-vanishing nature of scale factor, initial universe in finite means ruled out the initial singularity problem. The analysis of violation of energy conditions near the bouncing region and stability of the model shows that the matter bounce approach is highly unstable at the bounce but the rapid decay of perturbations away from the bounce supports the stability of the model.

Decidable $${\exists }^*{\forall }^*$$ First-Order Fragments of Linear Rational Arithmetic with Uninterpreted Predicates

First-order linear rational arithmetic enriched with uninterpreted predicates yields an interesting and very expressive modeling language. However, already the presence of a single uninterpreted predicate symbol of arity one or greater renders the associated satisfiability problem undecidable. We identify two decidable fragments, both based on the Bernays–Schonfinkel–Ramsey prefix class. Due to the inherent infiniteness of the underlying domain, a finite model property in the usual sense cannot be established. Nevertheless, we show that satisfiable sentences always have a model that can be described by finite means. To this end, we restrict the syntax of arithmetic atoms. In the first fragment that is presented, arithmetic operations are only allowed over terms without universally quantified variables. In the second fragment, arithmetic atoms are essentially confined to difference constraints over universally quantified variables with bounded range. We will call such atoms bounded difference constraints. As bounded intervals over the rationals still comprise infinitely many values, a trivial instantiation procedure is not sufficient to solve the satisfiability problem. After a slight shift of perspective, the positive decidability result for the first fragment can be restated in the framework of combinations of theories over non-disjoint vocabularies. More precisely, we combine first-order theories that share a dense total order without endpoints.

Is thirty-two three tens and two ones? The embedded structure of cardinal numbers

The acquisition and representation of natural numbers have been a central topic in cognitive science. However, a key question in this topic about how humans acquire the capacity to understand that numbers make ‘infinite use of finite means’ (or that numbers are generative) has been left unanswered. While previous theories rely on the idea of the successor principle, we propose an alternative hypothesis that children's understanding of the syntactic rules for building complex numerals—or numerical syntax—is a crucial foundation for the acquisition of number concepts. In two independent studies, we assessed children's understanding of numerical syntax by probing their knowledge about the embedded structure of cardinal numbers using a novel task called Give-a-number Base-10 (Give-N10). In Give-N10, children were asked to give a large number of items (e.g., 32 items) from a pool that is organized in sets of ten items. Children's knowledge about the embedded structure of numbers (e.g., knowing that thirty-two items are composed of three tens and two ones) was assessed from their ability to use those sets. Study 1 tested English-speaking 4- to 10-year-olds and revealed that children's understanding of the embedded structure of numbers emerges relatively late in development (several months into kindergarten), beyond when they are capable of making a semantic induction over a local sequence of numbers. Moreover, performance in Give-N10 was predicted by other task measures that assessed children's knowledge about the syntactic rules that govern numerals (such as counting fluency), demonstrating the validity of the measure. In Study 2, this association was tested again in monolingual Korean kindergarteners (5–6 years), as we aimed to test the same effect in a language with a highly regular numeral system. It replicated the association between Give-N10 performance and counting fluency, and it also demonstrated that Korean-speaking children understand the embedded structure of cardinal numbers earlier in the acquisition path than English-speaking peers, suggesting that regularity in numerical syntax facilitates the acquisition of generative properties of numbers. Based on these observations and our theoretical analysis of the literature, we propose that the syntax for building complex numerals, not the successor principle, represents a structural platform for numerical thinking in young children.

A New Regression Type Estimator and Its Application in Survey Sampling

In the present time, a large number of modified estimators have been proposed by authors to obtain efficiency. In this study, we suggested an alternative regression type estimator for estimating finite population means when there is either a positive or negative correlation between study variables and auxiliary variables. We obtained bias and mean square error equation of the proposed estimator ignoring the first-order approximation and found the theoretical conditions that make proposed estimator more efficient than simple random sampling mean estimator, product estimator and ratio estimator. In addition, these conditions are supported by a numerical example and it has been concluded that the proposed estimator performed better comparing with the usual simple random sampling mean estimator, ratio estimator and product estimator.

The Cortical Organization of Syntax.

Syntax, the structure of sentences, enables humans to express an infinite range of meanings through finite means. The neurobiology of syntax has been intensely studied but with little consensus. Two main candidate regions have been identified: the posterior inferior frontal gyrus (pIFG) and the posterior middle temporal gyrus (pMTG). Integrating research in linguistics, psycholinguistics, and neuroscience, we propose a neuroanatomical framework for syntax that attributes distinct syntactic computations to these regions in a unified model. The key theoretical advances are adopting a modern lexicalized view of syntax in which the lexicon and syntactic rules are intertwined, and recognizing a computational asymmetry in the role of syntax during comprehension and production. Our model postulates a hierarchical lexical-syntactic function to the pMTG, which interconnects previously identified speech perception and conceptual-semantic systems in the temporal and inferior parietal lobes, crucial for both sentence production and comprehension. These relational hierarchies are transformed via the pIFG into morpho-syntactic sequences, primarily tied to production. We show how this architecture provides a better account of the full range of data and is consistent with recent proposals regarding the organization of phonological processes in the brain.

Effect of Piezoelectric Transducers on the Resonator Frequencies of a Hemispherical Resonator Gyroscope

The boundary problem for the eigenvalues of the electroelasticity equations describing the oscillations of a cylindrical resonator of a hemispherical resonator gyroscope is solved by finite element means. The first ten resonator frequencies are determined under different boundary conditions where PZT-4 ceramics are used as piezoelectric transducers for the buildup and pickup of signals.

Principle of Unattainability of absolute zero temperature, the Third Law of Thermodynamics, and projective quantum measurements

The Principle of Unattainability rules out the attainment of absolute zero temperature by any finite physical means, no matter how idealised they could be. Nevertheless, we clarify that the Third Law of Thermodynamics, as defined by Nernst's heat theorem statement, is distinct from the Principle of Unattainability in the sense that the Third Law is mathematically equivalent only to the unattainability of absolute zero temperature by quasi-static adiabatic processes. This, on the one hand, leaves open the possibility of attainability of absolute zero by non-adiabatic means, without violating the Third Law. On the other hand, we point out some apparent incompatibility between the Postulate of Projective Measurement in quantum mechanics and the Principle of Unattainability in that projective measurements of energy could result in zero temperature.

Bayesian robustness to outliers in linear regression and ratio estimation

Whole robustness is a nice property to have for statistical models. It implies that the impact of outliers gradually vanishes as they approach plus or minus infinity. So far, the Bayesian literature provides results that ensure whole robustness for the location-scale model. In this paper, we make two contributions. First, we generalise the results to attain whole robustness in simple linear regression through the origin, which is a necessary step towards results for general linear regression models. We allow the variance of the error term to depend on the explanatory variable. This flexibility leads to the second contribution: we provide a simple Bayesian approach to robustly estimate finite population means and ratios. The strategy to attain whole robustness is simple since it lies in replacing the traditional normal assumption on the error term by a super heavy-tailed distribution assumption. As a result, users can estimate the parameters as usual, using the posterior distribution.

Finite quasi-barycentric means in an abstract setting

We provide, in a general setting without any algebraic and/or topological structure, a minimal axiomatic treatment of finite means which can be computed by a suitable weighted arithmetic mean. To this end, taking inspiration from Archimede’s theory of centre of gravity, we introduce, for non-null masses with finite support in an arbitrary non empty set Ω, the notion of quasi-barycentric mean, i.e. a map from the set of all such masses into Ω which satisfies the “intuitive” properties of consistency, shift-sensitivity and associativity (related to the barycentre of a system of material points). Moreover, we prove that it can be computed by the barycentre of finite distributions of masses in a (essentially unique) real vector space.